I found some information that you may find useful; credits go to Skeetendo for this information:

Quote:

In Pokémon Yellow, the player receives a special Pikachu that shows emotions, in a primitive form of the Happiness factor in G/S/C.

Gaining a level

+5 if current happiness < 100

+3 if current happiness < 200

+2 otherwise

Using, e.g., a Potion

+5 if current happiness < 100

+3 if current happiness < 200

+2 otherwise

Challenging a Gym Leader

+3 if current happiness < 100

+2 if current happiness < 200

+1 otherwise

Depositing in PC

−3 if current happiness < 200

−5 otherwise

Fainting

−1 (always)

There are two events in Pokémon Yellow that are based on its happiness. The first is on Pewter Museum’s top floor—a man whose daughter wants a Pikachu will say different things based on how happy the player’s is.
If happiness ≤ 100:

Your Pikachu looks untamed. May I have it for my daughter?

If happiness > 100:

I’d like to get that Pikachu off you, but it’s too attached to you.

The other instance is in Cerulean City. The character Melanie will reward the player with a Bulbasaur if Pikachu’s happiness is 147 or higher.